if you need to wear your boots while they're wet, get the heaviest garbage / largest sandwich-freezer bags you can find.. stick yer driest socks on, then use the boots..
this isn't the same, of course, as drying them, but i've done this many, many, many times when i knew i would be in wet areas (cold weather, also) & stayed fairly comfortable.
you'll get sweat damp. of course, if warm.
you'll get damp chill, if the boots are wet.
but you won't get wet-cold or wet guishy or bog-shat..
you can def put the boots back on, if there's not a prob with them freezing.
wearing wet boots in dry conditions is a reasonable way to dry them.
Goretex can be heat damaged, so be carefull of direct contact of the sole on a radiator, or overly hot hot air in the upper, if they're GTX lined.
wet boots in shitty weathers *suck*... sorry you & mamma nature had an episode..
stay warm!!
C